Homogenization of systems with equi-integrable coefficients. (8th August 2014)

• Record Type: Journal Article
• Authors: Briane, Marc; Casado-Díaz, Juan
• Is Part Of: ESAIM. Volume 20:Number 4(2014:Oct.)
• Page Start: 1214
• Page End: 1223
• Publication Date: 2014-08-08
• Subjects: Homogenization, -- vector-valued systems, -- not equi-bounded coefficients, -- equi-integrable coefficients, -- H-convergence; System analysis -- Periodicals; Calculus of variations -- Periodicals; Mathematical analysis -- Periodicals; Mathematical optimization -- Periodicals; Control theory -- Periodicals; 515.64
• DOI: 10.1051/cocv/2014013
• Languages: English
• ISSNs: 1292-8119

Abstract

Abstract : In this paper we prove a H-convergence type result for the homogenization of systems the coefficients of which satisfy a functional ellipticity condition and a strong equi-integrability condition. The equi-integrability assumption allows us to control the fact that the coefficients are not equi-bounded. Since the truncation principle used for scalar equations does not hold for vector-valued systems, we present an alternative approach based on an approximation result by Lipschitz functions due to Acerbi and Fusco combined with a Meyers L p -estimate adapted to the functional ellipticity condition. The present framework includes in particular the elasticity case and the reinforcement by stiff thin fibers.